I’m not sure if I can really answer your question, but I’m both a picker and a thumb-strummer, and I do each for different reasons. Full disclosure, I’m 6 months into TAC, but had some brief and informal guitar instruction in my late teens/early 20s. Which was some time ago! I never used a pick back then, simply didn’t have one.
Now, I tend to follow the instructional sessions as to what tool to use if any. There is a flat-picking course in the Courses section in the sidebar to the left of the screen; you might go there, I did. During practice sessions, when not specified, I tend to do whatever I feel like, or if I’ve mislaid the pick. (It’s usually on my desk or tucked between the strings on the headstock.) Some of the lessons I think would require using a pick if it’s got mixed strumming and single notes, unless you’re really dexterous with finger-picking; that is the only place where it could possibly slow you down.
But if you’ve been playing for 3-1/2 years, I’m sure you have your own habitual way that is comfortable and easy for you. But do try the flat picking course; it might address some of your concerns. Good luck!